XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/1/2026 9:45 PM, Richard Damon wrote:   
   > On 1/1/26 10:33 PM, olcott wrote:   
   >> On 1/1/2026 8:45 PM, André G. Isaak wrote:   
   >>> On 2026-01-01 16:48, Richard Damon wrote:   
   >>>> On 1/1/26 6:13 PM, Tristan Wibberley wrote:   
   >>>>> On 01/01/2026 22:40, Richard Damon wrote:   
   >>>>>   
   >>>>>> But it IS a theorem of the base system, as it uses ONLY the   
   >>>>>> mathematical   
   >>>>>> operations definable in the base system. What makes you think it   
   >>>>>> isn't a   
   >>>>>> Theorem in the base system.   
   >>>>>   
   >>>>> It has no derivation in the base system, if it had you wouldn't think   
   >>>>> the base system were incomplete.   
   >>>>>   
   >>>>   
   >>>> It has no PROOF in the base system.   
   >>>   
   >>> Which means it is not a theorem of the base system. A theorem is a   
   >>> statement which can be proven in a particular system.   
   >>>   
   >>   
   >> This is the kind of clarity that we need.   
   >> True in the base system essentially means   
   >> a theorem of the base system.   
   >   
   > Which s I explained, it is by at least the very normal definition.   
   >   
   > It is a statement of fact in the base system.   
   >   
   > And, that fact in the base system has been proven by a proof in some   
   > system that knows of the base system.   
   >   
      
   Has always been irrelevant.   
   Truth in the base system has always   
   actually been theorems of the base system.   
      
   That is the way that   
   "true on the basis of meaning expressed in language"   
   has always worked. When math diverged math erred.   
      
   > If you want to limit a "Theorem" to only be a something provable in the   
   > base system then it is merely a True Statement in the base system, which   
   > the system can not be proven.   
   >   
   So when we directly encode all semantics   
   in the formal language such that   
   ∀x ∈ F (Provable(F,x) ≡ True(F,x))   
   Then incompleteness ceases to exist   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)